The Family Computer Disk System (often shortened to Famicom Disk System or just the Disk System) is an accessory for the Family Computer. It allowed the Family Computer to play certain games on a floppy disk rather than a cartridge. Floppy disks had the advantages of being cheaper. Besides that, the disks were rewritable, making saving easier.
Sharp Corporation, a Japanese Electronics and Domestic Appliance company, created the Twin Famicom, a Family Computer combined with the Disk System into one piece of hardware, but it was also only released in Japan.

The main reason for the FDS's Japan-only release is believed to be due to a lack of success caused by various issues:[1]

The games were easier to pirate, due to the low amount of copy protection (i.e. recognizing legitimate disks by an empty space on the bottom).

The games were easier to damage, as floppy disks were sensitive to magnetic wavelengths and exposed the strip that lets the system recognize and run the game. In the latter case, the strip could get scratched, dirty, or even grow mold in severe cases.

Because of the enhanced sound qualities, audio was hard to convert when the games were ported to cartridges.

The games had lengthy loading times at various points (often when swapping sides, or when entering an area that cannot be processed easily).

Most games required the player to eject the disk at various points, flip them over, and re-insert them (often after the title screen and on the game's final stretch), similarly to how various PlayStation games require the player to eject and swap optical disks at certain points.

The jewel cases that contained the games were smaller than cartridge boxes, and were therefore easier to overlook in stores or lose in homes. The cases were also required to fully protect the disk, whereas cartridges could be stored, standalone, on shelves.

Nintendo might've had plans to make an NES version of the Disk System, as there is a port on the bottom of the original NES that went unused.